Answer
See below.
Work Step by Step
Step 1. Given $f(x)$ is an odd function, we have $f(-x)=-f(x)$.
Step 2. Given $g(x)$ is an even function, we have $g(-x)=g(x)$.
Step 3. Use the given information, we have $f(-1)=-f(1)=2$, $g(1)=g(-1)=2, g(2)=g(-2)=0$
Step 4. $f(g(-1))=f(2)=1$, $f(-2)=-f(2)=-1$, $f(g(-2))=f(0)=0$, $f(g(1))=f(2)=1$, and $f(g(2))=f(0)=0$,
Step 5. See filled table.
